The room-temperature synthesis of AZPbBr3 QDs proceeds through rapid injection of an aziridine solution in chloroform or dibromomethane (see further details in Figure 1b and the Supporting Information) into a precursor solution comprising PbBr2/TOPO adduct, diisooctylphosphinic (DOPA) and alk(en)ylcarboxylic acids (2-ethylhexanoic acid, oleic acid or erucic acid) in hexane, with optional addition of alkylphosphonic acids (for obtaining the smallest NCs, see subsequent discussion). We note that AZ cations cannot be formed ex-situ for use as a stable precursor due to their high ring instability in common solvents. Instead, AZ cations form in situ owing to the high acidity of the PbBr2/TOPO precursor solution (aziridine:DOPA:carboxylic acids=1:8.5:17, molar ratios). TOPO, DOPA, and alkyl carboxylic acids are known as weakly binding ligands for perovskite NCs.24 They can be readily displaced by more strongly binding alternatives such as didodecyldimethylammonium bromide (DDAB),26, 27 custom-engineered zwitterionic phospholipid ligand [2-octyldodecylphosphoethanolamine (C8C12-PEA)],25 or the commercially available natural phospholipid lecithin,28 followed by purification and isolation steps. This procedure yields stable colloids of highly monodispersed cuboidal AZPbBr3 NCs exhibiting bright green emission and high stability over long-term storage in air (Figure S1).
The size of NCs was adjusted between 4.5 nm and 14 nm in diameter, resulting in tunable absorption and PL, with PL peaks in the range from 498 nm to 530 nm (Figure 1c, d, S2, S3, and Table S1) by manipulating the reaction time (the time delay between the injection of the aziridine solution and the injection of the ligand solution was typically 10-240 seconds) as well as by introducing various amounts of alkylphosphonic acids (hexyl-, octyl-, decyl-, or dodecylphosphonic acid) into the PbBr2/TOPO precursor solution. Phosphonic acids slow down the reaction kinetics, facilitating the preparation of strongly confined AZPbBr3 NCs (down to 4.5 nm, Figure S2d). Conversely, utilizing mesitylene as a reaction solvent and a longer reaction time yields NCs larger than 10 nm, with PL peaks from 525 nm to 530 nm. The overall dilution of precursors does not significantly alter the PL peak of AZPbBr3 (Figure S2c), unlike in the synthesis of CsPbBr3 NCs.24 Importantly, a narrow size dispersion of AZPbBr3 NCs can be reached only under a high Pb-precursor excess (aziridine:Pb=1:4, molar ratio). The minute-scale formation kinetics of AZPbBr3 NCs allow in-situ optical monitoring with UV-vis absorption, as exemplified for 6.5-nm samples (Figure S4).
DDAB-capped AZPbBr3 NCs are sharp cuboids, in agreement with the known tendency of cationic ligands to stabilize the set of (100) facets.26, 29, 30 C8C12-PEA-coated NCs are rather truncated, presumably due to surface reconstruction or etching (Figure S3, Table S1). Lower colloidal robustness was observed when employing the recently reported dicationic ligands (propanediyl-1,3-N, N-bis (didodecylmethylammonium bromide), C3-4C12AB)31 or lecithin. The AZPbBr3 NCs capped with DDAB or C8C10-PEA exhibit an average PL QY of 80 ± 2% for NC sizes between 8 nm and 10 nm, and the PL QY increases up to 90 ± 4% for samples prepared with the addition of phosphonic acids (4.5-8 nm). The high-angle annular dark field-STEM (HAADF-STEM) and high-resolution HAADF-STEM images evidence the (100)-termination of the DDAB-capped NC surfaces (Figure 1e; synthesis without phosphonic acids, 20 seconds-reaction labeled as "standard" in Table S1). Shape retrieval from small-angle X-ray scattering (SAXS, Figure 2a) yields a slightly prolate cuboid shape (aspect ratio of ca. 1.04) with the lengths of the three NC edges being 8.27 ± 0.12 nm, 8.28 ± 0.93 nm, and 8.60 ± 0.48 nm (that is, substantially isotropic; see Supporting Information, Figure S5 and Table S2 for SAXS-data of an extended NC size series).
Figure 1f presents the size-dependence of the band-gap energies in AZPbBr3, using the QD size determined via TEM and the band gap estimated from the second derivative of the absorbance (see Supporting Information for details). Such a “sizing curve” is of great practical utility as an express method for obtaining the approximate QD size using a standard UV-VIS spectrometer only. Furthermore, the size dependence connects to the basic electronic structure of the underlying bulk material. Within the semi-empirical expression derived in Aubert et al.,32 the functional form of the size dependence for a wide range of semiconductors is given by only three bulk parameters: the bulk band gap , the Bohr diameter , and the dielectric constant at the optical frequency. In Figure1f, we have tested the inverse of this idea by fitting our experimental AZPbBr3 size-dependent band gap (open squares) with the semi-empirical expression (solid line) given by Aubert et al., hereby yielding approximate estimates for the thus far still ill-defined electronic parameters for bulk AZPbBr3. To limit the parameter space and stabilize the fit, we only keep the bulk band gap as a free fit parameter and estimate both the exciton Bohr diameter and the dielectric constant at the optical frequency with the help of DFT calculations (see Supporting Information for details, Tables S4 and S5). We obtain a reasonable agreement with the experimental size dependence for the following parameters: =2.35 eV (fitted), =7.8 nm (fixed; estimated via DFT), and =7.3 (fixed; assumed identical to CsPbBr3)33. Overall, we conclude that the electron and hole effective masses, dielectric constant, and, thus, the exciton Bohr diameter should be comparable in AZPbBr3 and CsPbBr3, while the bulk band gap in AZPbBr3 appears slightly lower ( =2.38 eV in CsPbBr3)34. We also note that a previous estimate for the bulk AZPbBr3 band gap by Petrosova et al.13 found an even lower value (2.27 eV); however, a different definition for the band gap (via the zero-crossing in a Tauc plot) precludes a direct comparison to the values found by us for AZPbBr3 NCs and by Mannino et al. for CsPbBr3 (in both cases utilizing second derivatives).
The crystal structure of AZPbBr3 NCs suspended in cycloheptane was investigated with synchrotron X-ray total scattering methods. Bulk AZPbBr3 was previously reported to crystallize in the cubic lattice with a space group symmetry and ordered Br atoms with a straight Pb-Br-Pb bond angle of 180°.13 However, evidence of local and dynamic symmetry breaking has been found in various lead-halide perovskites that exhibit a long-range cubic structure.35-39 We account for local symmetry breaking with a split-cubic perovskite model, for a disordered AZ cation with a cuboctahedral cluster, and for disorder as well as a cuboidal NC morphology with the Debye scattering equation. The resulting fit to the wide-angle X-ray total scattering (WAXTS) data is shown in Figure 2b, together with a 2D map of the refined bivariate lognormal size-distribution function. Figure 2c displays the obtained structure, with Pb-Br-Pb bond angles deviating by 13° from the 180° angle expected for an ideal cubic structure. Deviations of similar magnitude are also found in FAPbBr3, FAPbI3, and FASnI3 NCs,8, 12, 40-42, corroborating that AZPbBr3 NCs share the locally broken crystal symmetry. Furthermore, AZPbBr3 NCs exhibit a slight lattice expansion of about 0.10% to 0.15% with respect to the bulk value, similar to many other nano-sized samples of lead-halide perovskites (Table S3).43-45 We further uncover signs of a non-cubic long-range structure. A small deviation in lattice parameters from a cubic cell (with the c axis about 1% larger than the a=b axis) suggests that the average cell is tetragonal (see Figure S6 and the pertinent discussion in the Supporting Information).
To further understand the crystal symmetry, we performed variable-temperature WAXTS measurements of dried NCs loaded into a glass capillary and collected 93 WAXTS scattering patterns (at 3 K steps, from 11 K to room temperature; see Supporting Information). Similar to the RT WAXTS data of the solution-phase NCs, also the RT crystal metrics of the dried NCs suggest a distortion from the cubic lattice when analyzed according to the structureless Le Bail method (which avoids the occurrence of the non-random orientation distribution function of the NCs and is fully unbiased by errors in the structural model). With decreasing temperature, the crystal unit cell volume monotonously decreases. More importantly, an additional symmetry change is found below 90 K (Figure 2d). From 90 K to 11 K, the peak widths progressively increase (Figure 2e), suggesting an additional peak splitting (partially hidden under the broad Bragg peaks), in line with a symmetry-lowering transition to an orthorhombic metric, observed also in other 3D lead halide perovskites.
Having elucidated the experimentally observed crystal structure of the synthesized AZPbBr3 NCs, we further consider the crystal stability via a computationl approach. The Goldschmidt tolerance factor (t)46 is used extensively to predict the formation and stability of the perovskite structure. However, some studies suggested that a revision of the Goldschmidt tolerance factors may be required.47 Recently, Bartel et al. introduced a new tolerance factor48
with nA representing the oxidation state of cation A and a value of τ < 4.18 suggests a perovskite structure. We estimated τ = 3.30 for AZPbBr3, further supporting the perovskite structure formation (the ionic radii used in the present work were rBr = 196 pm, rPb = 119 pm, rAZ = 227 pm, and nAZ = 1).
To investigate the stability of AZPbBr3, we considered the formation reaction equation (CH2)2NH2Br + PbBr2 ® (CH2)2NH2PbBr3 and the corresponding reaction enthalpy:19
ΔHr = Etot[(CH2)2NH2PbBr3] – Etot[(CH2)2NH2Br] – Etot[PbBr2] (2)
A negative reaction enthalpy would indicate a stable perovskite structure. To obtain the total energy (Etot) of the reactant and products, we performed density functional theory (DFT) calculations, employing the PBE exchange-correlation functional with van-der-Waals (vdW) corrections. We further considered an orthorhombic AZPbBr3 crystal structure, the most stable phase at such 0 K calculations, in coarse agreement with the lower-than-tetragonal symmetry in our low-temperature X-ray total scattering data (see Supporting Information for further details, including a discussion on the likelihood of polymorphism). We then obtained negative ΔHr values of -0.362 eV and -0.373 eV with and without spin-orbit coupling, respectively, affirming the stability of AZPbBr3. The respective electronic-structure calculations evidence a direct band gap of AZPbBr3. The conduction band originates from Pb-p orbitals, while the valence band is predominantly of Br-p character, consistent with other lead halide perovskites (see Supporting Information for details, Figures S7 and S8, and Tables S6 and S7).
The ligand chemistry of C8C12-PEA and DDAB-capped AZPbBr3 NCs was elucidated with NMR experiments performed in solution and the solid state. 1H solution NMR spectra for both C8C12-PEA and DDAB-capped AZPbBr3 NCs confirm the presence of the corresponding capping ligand (Figure 3a). DDAB-capped NCs do not sustain more than one washing cycle, after which a free alkyl carboxylic acid (in this case – oleic acid) is still detected in the DDAB-sample (as alkenyl protons at 5.4 ppm). We thus inspected the C8C12-PEA-capped NCs in greater detail since they can be purified at least three times without a notable loss of NC dispersibility. Already twice-washed samples lack any oleate-related signal. 31P NMR spectra evidence the surface-bound C8C12-PEA ligands in solution (Figure 3b) and solid state (Figure S10b). The twice-washed C8C12-PEA-AZPbBr3 sample shows only a broad signal centered around -1 ppm from bound C8C12-PEA (Figure 2b, top). No other signals were detected, excluding free or surface-bound TOPO and DOPA. We also analyzed the NCs synthesized with the addition of alkyl phosphonic acids (Figure 3b, middle), whose 31P NMR signal is expected at 25-28 ppm (see the octylphosphonic acid spectrum in Figure S9 and Ref49). Colloids washed only once exhibit a broad surface-bound C8C12-PEA signal at -1 ppm and three narrow peaks in the range of 40-60 ppm (absent in double-washed NC samples), originating from the residual TOPO (49 ppm) and DOPA (57 ppm and 43 ppm for its main impurity). These NC cores were then digested by the addition of DMSO-d6, liberating surface-bound species, leading to a narrow signal from the free C8C12-PEA ligand (Figure 3b) and solvent-related shifts from the TOPO/DOPA species, but still no signatures of phosphonic acids. We thus conclude that the small quantities of alkylphosphonic acids used in the synthesis are fully removed upon washing and do not bind to the NC surfaces.
The presence and integrity of the AZ cation in AZPbBr3 NCs were characterized with 1H solid-state NMR spectra (Figure S11a). The bulk material features two main peaks at 4 ppm and 6 ppm. Additional minor species are resolved at 5 ppm and 8 ppm, although the material was phase-pure according to powder XRD (Figure S12). No NMR signal from possible ring-opened alkyl ammonium was detected. The observed species were also found in the AZPbBr3 NCs in solution and solid-state 1H measurements, with the addition of the alkyl protons from the ligands at 2 ppm (Figure 3a and Figure S10a). 207Pb solid-state NMR is highly sensitive to deviations from a cubic crystal structure in lead halide perovskites. Experiments on bulk AZPbBr3 show a single signal centered around 485 ppm with a full width at half maximum (FWHM) of 13.1 kHz, similar to the cubic FAPbBr3 signal (Figure S11b)50. The 207Pb solid-state NMR signal for C8C12-PEA-capped AZPbBr3 NCs fits very well with the bulk reference, exhibiting a single signal around 505 ppm with a FWHM of 16.5 kHz (Figure 3c). Broader peaks in NCs compared to bulk have previously also been reported for CsPbBr3, likely caused by the increased disorder and higher ion mobility.50
Raman spectra of AZPbBr3 NCs and AZPbBr3 bulk powders confirm the presence of the AZ cation within the Pb-Br perovskite cage. Beyond the dense and almost featureless spectrum of bands below150 cm-1, characteristic for the Pb-Br framework in 3D lead-bromide perovskites,51 both NCs and bulk exhibit a band at about 308 cm-1, a doublet at 807 cm-1 and 871 cm-1, and a band at 1227 cm-1, previously assigned to the AZ-cage mode, ring deformation, and ring stretching, respectively.15
Only a limited amount of degradation products related to AZ ring opening was detected (Figure S13 and Table S8). It is worth noting that some bands remain challenging to assign due to the lack of Raman measurements conducted explicitly on the AZ-cation, which is unstable outside the perovskite framework. Notwithstanding these uncertainties, Raman spectroscopy also evidences the AZ cations incorporated in the Pb-Br framework, both in AZPbBr3 NCs and bulk.
Room-temperature optical properties of AZPbBr3 NCs, here also referred to as QDs due to their quantum-light emission capabilities (vide infra), were examined via single-particle PL spectroscopy in a home-built inverted oil-immersion microscope (see details in the Supporting Information). Such PL studies at the single-QD level unveil basic structure-property relationships52 as well as sample heterogeneities53 and temporal fluctuations54, 55 of emitters, which are otherwise unresolved in the ensemble spectra. Figure 4a shows a single-particle PL spectrum of an AZPbBr3 QD capped by branched C8C12-PEA ligands. Fitting a Lorentz function to the experimental data returns an emission peak centered at 512 nm and an FWHM of 82 meV, demonstrating the spectrally narrow emission of individual AZPbBr3 QDs. Measurements were performed in a nitrogen atmosphere for extended spectral photostability, as evidenced in the PL spectra series in Figure 4b. AZPbBr3 QDs exhibited high single-photon purity, confirmed by a strongly suppressed peak at a delay time of zero in the second-order photon-photon correlation function g(2)(t) (Figure 4c). The high single-photon purity with g(2)(0)=0.1 is on par with FAPbBr3 and MAPbBr3 QDs capped by the same C8C12-PEA ligand.25 Furthermore, we quantify the PL intensity fluctuations, termed "PL blinking", i.e., the stochastic switching between a bright (ON) and a dimmed (OFF) state. PL blinking roots in a photo-induced charge trapping at surface defects, possibly mediated by efficient Auger-Meitner recombination, and could be strongly affected by the QD surface passivation.56 The fraction of time spent in the ON state (ON fraction) is, therefore, a suitable metric of the surface quality for the nanomaterial under study at the single-QD level. Recently, we demonstrated that the C8C12-PEA ligands stabilize hybrid organic-inorganic lead halide perovskite QDs and enable emission at the single-particle level with >90% ON fraction.25 A blinking trace from a single C8C12-PEA-capped AZPbBr3 QD (Figure 4d) also exhibits a high ON fraction (~95%), representative of the high ON fraction (typically > 85%) for AZPbBr3 QDs with this ligand capping (Figure 4h). We then surveyed the blinking behavior of QDs capped by various alternative and post-synthetically attached ligands, i.e., zwitterion lecithin (Figures 4e), monocationic DDAB (Figure 4f), and dicationic C3-4C12-AB (Figure 4g). Although C8C12-PEA and lecithin are both zwitterionic phospholipids, lecithin-capped QDs exhibit longer OFF events and a significantly smaller ON fraction than C8C12-PEA-capped QDs, symptomatic for the compromised surface passivation of the former. We attribute the superior performance of C8C12-PEA to the better fit of its primary ammonium binding group into the A-cation site at the QD surface.25, 30 Likewise, blinking traces of QDs capped by one of the two quaternary ammonium ligands, DDAB or C3-4C12-AB, displayed smaller ON fractions than the C8C12-PEA-capped QDs. We further observed that all samples, except C8C12-PEA-capped QDs, feature large QD-to-QD variation in the ON fraction (Figure 4h). This could be assigned to the sample preparation procedure needed for single-QD spectroscopy, which requires a strong dilution (by a factor of about 50,000) of the colloids.
The dilution step can also alter the QD morphology57 and induce a blue shift of the PL energy (Figure S14). Occurring under water-free and inert conditions, structural and optical alterations upon dilution are rationalized considering ligand desorption enhanced by the dynamic ligand binding observed in ionic perovskite QDs.58 Dilution-induced alterations can also explain the deviation of ON fractions for the different ligands despite comparably high PL QYs in the undiluted ensemble (Figure S14). Single-particle spectroscopy thus acts as a stress test for ionic QDs with inherently dynamic ligand binding that is better endured by C8C12-PEA-capping. The reduced blinking for such a ligand formulation could be exploited for the realization of single-photon sources without the loss in the single-photon purity.59
While room-temperature single-QD experiments unveiled the optimal ligand choice, the intrinsic electronic properties of the semiconductor core are probed at cryogenic temperatures. At 4 K, the perturbation by phonons via exciton-phonon coupling is highly suppressed, enabling observation of the exciton fine structure arising from electron-hole exchange interaction, as well as emission from exciton complexes. We studied single AZPbBr3 QDs capped with C8C12-PEA, DDAB, or lecithin
ligands. Single QDs with ensemble QD sizes from about 7 nm to 9 nm exhibit exciton PL bands in the range of 2.31 eV to 2.20 eV (537 nm to 564 nm), with a FWHM ranging from 0.2 meV to 0.8 meV (where 0.2 meV is our setup resolution). Among the studied ligand systems, only DDAB- and C8C12-PEA-capped single QDs exhibit a spectrally stable multi-line exciton spectrum with sub-meV spectral diffusion (Figure 5a). The multi-line spectrum is ascribed to the bright triplet character of excitonic emission in lead halide perovskites.7, 60 By introducing a linear polarizer in the collection path and recording the angle-dependent exciton intensities, we obtained the polarization profile typical for a bright triplet exciton: individual exciton sublevels are highly linearly polarized and orthogonal to each other, as in the example displayed in Figure 5b. Across various single QDs, we observed both doublet and triplet exciton fine-structure (see insets of Figures 5c and 5d). Splitting energies of doublet (∆) and triplet (∆1 and ∆2) exciton fine-structures are plotted as a function of the exciton energy in Figures 5c and 5d, respectively. Splitting energies vary from 0.2 meV to 1.4 meV for QDs with PL peak ranging from 2.21 eV to 2.31 eV. In addition to a systematic trend of increasing splitting energies with increasing exciton energy, large variations in splitting energy are observed for a given exciton energy. This variation was also reported in other lead halide perovskite QDs,6, 7, 60-64 and suggests that the exciton fine-structure splitting is sensitive to the shape anisotropy of the studied QDs. In general, exciton properties of AZPbBr3 QDs are comparable to CsPbBr37, 65, 66 and FAPbBr3 QDs.60, 67 Compared to the C8C12-PEA- or DDAB-capped single QDs, lecithin-capped QDs exhibit stronger spectral diffusion (~ 10 meV, see Figure S15), consistent with their more pronounced PL blinking and lower ON fraction at room temperature.
To quantify the quantum correlations among photogenerated exciton complexes, we drive the single QDs under high excitation fluence, hereby obtaining emission also from trion (X*) and biexciton (XX); see one example in Figure S16a. As the excitation fluence increases from to , two additional peaks emerge on the lower-energy side of the exciton emission spectrum, which are assigned to the trion (red-shifted from Ex by 25 meV) and biexciton (red-shifted from Ex by 40 meV). Summarizing the results from all studied single QDs, binding energies of trion ( ) and biexciton ( ) are plotted as a function of the exciton energies (see Figure S16b). increases from 10 meV to 25 meV for exciton energies increasing from 2.20 eV to 2.30 eV, and increases from 30 to 40 meV for exciton energies increasing from 2.24 eV to 2.30 eV. Qualitatively, the observed trend of increasing or with increasing exciton energy is universal in semiconductor QDs68, 69 as the Coulomb interaction among photo-generated charge carriers is steadily enhanced with decreasing QD size. Quantitatively, the size-dependent trends of and are similar to those reported for FAPbBr3 QDs.70 Utilizing the obtained knowledge of in AZPbBr3 QDs, we performed single-QD anti-bunching experiments under high excitation (0.3 ) with and without filtering the biexciton emission. When the spectrum is unfiltered (Figure 5e, dark grey line), no anti-bunched emission was observed, i.e., g(2)(0)~1, suggesting very efficient biexciton emission at 4 K. When the biexciton emission is discarded by spectral filtering (Figure 5e, blue line), emission is characterized by a regular stream of single photons (g(2)(0) ~ 0, within the noise floor of ~0.1). In addition, all the studied individual AZPbBr3 QDs feature a mono-exponential PL decay with lifetimes between 400 ps and 1600 ps, as shown in Figure S17. These lifetimes are much longer than reported in CsPbBr3 QDs, suggesting the absence of a pronounced giant oscillator strength,7 probably related to the softer and more dynamic lattice of the AZPbBr3 QDs.